InterviewSolution
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InterviewSolution
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`lim_(n->oo)1/n[1/(n+1)+2/(n+2)+....+(3 n)/(4 n)]`A. log4B. `-log4`C. `1-log4`D. None of these |
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Answer» Correct Answer - D `underset(nrarroo)(lim)(1)/(n)((1)/(n+1)+(2)/(n+2)+...+(3n)/(4n))` `=underset(nrarroo)(lim)(1)/(n)(((1)/(n))/(1+(1)/(n))+((2)/(n))/(1+(2)/(n))+...+((3n)/(n))/(1+(3n)/(n)))` `=underset(nrarroo)(lim)(1)/(n)sum_(r=1)^(3n)(((r)/(n))/(1+(r)/(n)))=int_(0)^(3)(x)/(1+x)dx` `=int_(0)^(3)(x+1-1)/((1+x))dx=int_(0)^(3)dx-int_(0)^(3)(1)/(1+x)dx` `=[x-log(x+1)]_(0)^(3)=3-log4` |
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